Chemical Kinetics
Chemical Kinetics tests order determination, integrated rate laws, half-life, and Arrhenius reasoning.
Rate laws and order
- rate = k[A]^m[B]^n; order is experimental and is not read off the balanced equation
- molecularity belongs to an elementary step and is always a small whole number
- zero order: [A] = [A]0 − kt, t½ = [A]0/2k (depends on initial concentration)
- first order: k = (2.303/t)log(a/(a − x)), t½ = 0.693/k (independent of concentration)
- units of k: mol L⁻¹ s⁻¹ (zero), s⁻¹ (first), L mol⁻¹ s⁻¹ (second)
Arrhenius and collisions
- k = A·e^(−Ea/RT); log(k2/k1) = Ea/2.303R × (1/T1 − 1/T2)
- a plot of log k against 1/T has slope −Ea/2.303R
- temperature coefficient is roughly 2–3 per 10 K for many reactions
- a catalyst lowers Ea and speeds both directions; it does not shift K or ΔH
Worked example
A first-order reaction is 75% complete in 60 min. Then a − x = 25 when a = 100. k = (2.303/60)log(100/25) = (2.303 × 0.602)/60 = 0.0231 min⁻¹. Hence t½ = 0.693/0.0231 = 30 min, exactly half of the 75%-completion time as expected for first order.
Traps that cost marks
- Using stoichiometric coefficients as reaction orders.
- Forgetting that ester hydrolysis in a large excess of water is pseudo-first-order and k is unchanged by water concentration.
- Mixing the zero-order and first-order half-life expressions.
- Claiming a catalyst increases the yield; it only shortens the time to equilibrium.